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Yes, it is. But it's absolutely far from worth it.

Here's my advice; I took to a second complete playthrough of almost exactly the same path (Iconoclast with a focus on balancing as many companions as I could) as my first to see if it was possible to actually get those cool rep rewards from the Act 4 factions in a single playthrough. It is possible to max all of these factions without using toybox or exploiting any mechanics (using, yes, exploiting, no)

Here's how I did it:

Step 1: What's actually not as important as you think is min-maxing your cargo. The only time it becomes important is at breakpoints where you'll get JUST enough reputation to activate a colony project that boosts rep.

Step 2: Prioritize colony projects that boost rep. It is possible to infinitely farm your way to max rep but these will save you days of grinding. ALWAYS pick Drusians if given a choice between factions to dump rep into. They are far-and-away the hardest faction to grind up and have arguably the best late-game rewards.

Step 3: After completing many colony projects that are considering "event worthy" you'll be asked to enter into a conversation in which there are certain different rewards that the game tells you to pick from before making the choice. I CANNOT STRESS THIS ENOUGH ALWAYS CHOOSE THE TALK TO YOUR ADVISORS OPTION PRIOR TO MAKING THIS CHOICE. Not only will this remove a lot of the negative penalties from the existing options but also add new options or additional bonuses to the existing ones (namely, rep gains, some as big as 5000).

Step 3: Remember that last step? Well, there's one colony project that's more important and that's the projects that give a repeated drop of resources. Chirurgeon Medkits, Scrocher, Iron Eye Grenades take ALL of them. These are how you're going to be able to max Pirates, Kasablica, and Explorators. These will give you a steady supply of cargo materials in the ranged weaponry and mechanicus creations category that are produced indefinitely. All you need to do is warp jump a safe route about 10 or so times back and forth and they will reset. Add to cargo, turn in, rinse and repeat. This is mindless but fairly painless and combined with some of the 20k reputation projects these factions can all be reasonably maxed without tearing your hair out. This is also coupled with the fact that most of your cargo from Act 3 is Xenos Artifacts which can be turned in to Pirates or Kasablica to get a nice jump on either.

Step 4: Imperial Navy is straightforward and while maxxing them is kinda pointless it's also just going to happen naturally if you're maxing the others. Once you've exhausted all space combat encounters you won't have enough to turn in for max rep and NEVER waste any projects that lock you out of other rep rewards for the navy. All you have to do is repeatedly spam warp paths until one of your colonies triggers a random event that requires your attention. Some of these are space battles. Simply take part in them, win them, and turn in the cargo you win. These triggered regularly for me until I maxxed my rep. Then, they stopped appearing. Either the devs thought of this or I'm a very unlucky boy.

Step 5: So what about the Drusians? Well, two things. Step 1 still mostly applies but pay special attention to Holy Artifacts, Jewelery, and Ship Components. Dump ALL of these into the Drusians and do the same for as many melee weaponry and armor kit cargo as you can. How do you farm Drusians if none of the replenishing resources go to cargo for them? Well, you have to farm random void encounters and these are PAINFUL. Only do this once you've exhausted all other options because this process took me a solid 20 hours to complete. The encounters you'll want are mainly the ones with the Khorne followers on the lower deck as this grants a steady supply of axes and chainmail to gift to the Drusians for that sweet sweet rep (The nurgle encounter also gives a decent supply of chainmail). Only some of the encounters actually drop any cargo-able loot and some will drop ranged weaponry. The only way to speed this up I've found is; Use orange routes instead of yellow ones as they spawn encounters more frequently without dinging your ship too much, turn on fast combat speed in settings and bring character(s) who can take advantage of Finest Hour so you can kill everything before they get a chance to respond (Pasqual with a Plasma Rifle and Cassia work perfectly suitably), and just brute force bad encounters as opposed to trying to re-roll as it's faster just to spend a minute in a bad encounter than trying to sit through 4 different load screens fishing for a good one.

Anyways, if you optimize better than I did you'll grind less than I did. I didn't realize just how much harder the Drusians were and if I focused on them from the word-go this is nearly painless as you'll just be clicking your way to max rep with most factions.

Enjoy your shiny new toys fellow rogue traders.